# POISSON

## Content

This function returns the Poisson distribution.

## Syntax

`POISSON(x, mean, cumulative)`

## Arguments

This function has these arguments:

| Argument | Description |
| -------- | ----------- |
| *x* | [Required] Number of events. Provide an integer, or the value is truncated. The number must be greater than zero. |
| *mean* | [Required] Expected numeric value. The number must be greater than zero. |
| *cumulative* | [Required] Set to TRUE to return the cumulative Poisson probability that the number of random events occurring is between zero and *x* inclusive. Set to FALSE to return the Poisson probability mass function that the number of events occurring is exactly *x*. |

## Remarks

The cumulative Poisson probability is calculated as follows:

![](https://cdn.mescius.io/document-site-files/images/8d606653-16a0-474d-b9dc-e2b4d01c2446/images/Func-POISSON-True.png)

The Poisson probability mass function is calculated as follows:

![](https://cdn.mescius.io/document-site-files/images/8d606653-16a0-474d-b9dc-e2b4d01c2446/images/Func-POISSON-False.png)

where x is the number of events ( *x* argument), and mu is the mean ( *mean* argument).

## Examples

`POISSON(A3,B4,TRUE)`
`POISSON(R1C2,3,FALSE)`
`POISSON(7,4,TRUE)` gives the result 0.948866384
`POISSON(7,4,FALSE)` gives the result 0.059540363